Ramification theory from homotopical point of view, I

Tomoyuki Abe

Ramification theory from homotopical point of view, I

Algebraic Geometry 2026-02-02 v2 Category Theory Number Theory

Authors: Tomoyuki Abe

Abstract

We prove the compatibility of pushforward along a proper morphism of an \'{e}tale constructible sheaf and the pushforward of its characteristic cycle up to $p$ -torsion. This was conjectured by Takeshi Saito. For this, we revisit the construction of the characteristic cycle, due to Saito and Beilinson, from more homotopical point of view. In particular, the language of $\infty$ -categories is indispensable to carry this out.

Keywords

ramification theory étale constructible sheaf characteristic cycle proper morphism ∞-categories pushforward

Cite

@article{arxiv.2206.02401,
  title  = {Ramification theory from homotopical point of view, I},
  author = {Tomoyuki Abe},
  journal= {arXiv preprint arXiv:2206.02401},
  year   = {2026}
}

Comments

Some proofs were simplified based on the referee's feedback. See the Introduction for further details on these changes

Ramification theory from homotopical point of view, I

Abstract

Keywords

Cite

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